Place the rinsed and destemmed plums in a 6-quart stockpot.
Stir in the water and the cardamom pods.
Cook over medium heat and bring to a boil; reduce heat to low and simmer for 1 hour.
Remove from heat and allow the plums to completely cool.
Place a colander on top of a large deep bowl.
Once the plums have cooled, pour them into the colander.
Strain the plums by pressing them with your hands against the colander.
Pick up the remaining fruit slurry in the colander by the handfuls and squeeze the pulp, skins, and cardamom seeds into the bowl with the syrup, retaining the pits and cardamom shells and then discarding them.
Put the plum mixture back into the stockpot, stir in the sugar, and bring the mixture to a boil over medium-low heat.
Turn the heat down to low and let it simmer for 3 hours, or until the mixture has thickened.
Stir it every 20 to 30 minutes.
In the meantime, prepare the canning jars.
Preheat oven to 200°F.
Wash the jars with soap and water, dry them, and place them mouth side up, without lids, in the oven for 10 minutes.
Sterilize the lids by putting them in a bowl and pouring boiling water over them. Allow to dry.
Spoon the hot plum jam into the hot, sterilized jars and seal.
Allow jars to cool to room temperature.